1. Yes, I believe the dups are using space.
2. I once had this happen. My solution was to unclick sync photos in iTunes; you will get a popup asking if to delete photos on phone. I selected yes. After sync, there will be no photos on phone. Now select to sync photos again and re-sync. Photos from Photos app will be added to phone. Caveat: photos added by syncing from Photos app can't be deleted on the phone - only by deleting in Photos and re-syncing. PITA.
3. If you mean how to stop backing up to Mac, just unclick sync photos as in #2 but keep photos on phone. Then turn on iCloud Photo Library: Settings > Photos & Camera > iCloud Photo Library on.

Photos on iPhone and Mac is overly complicated if you ask me. There may be some other solution for you as well. Let's hope others will chime in.

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